Learning Disease-Sensitive Latent Interaction Graphs From Noisy Cardiac Flow Measurements

Cardiac blood flow patterns contain rich information about disease severity and clinical interventions, yet current imaging and computational methods fail to capture underlying relational structures of coherent flow features. We propose a physics-informed, latent relational framework to model cardiac vortices as interacting nodes in a graph. Our model combines a neural relational inference architecture with physics-inspired interaction energy and birth-death dynamics, yielding a latent graph sensitive to disease severity and intervention level. We first develop the method using computational fluid dynamics simulations of aortic coarctation, where learned interaction graphs reveal increasingly structured vortex interactions as vessel narrowing progresses. The resulting graph entropy exhibits a strong monotonic relationship with coarctation severity ($R^2=0.78$, Spearman $|ρ|=0.96$). We then evaluate the framework on fluid-structure interaction simulations of intracranial aneurysms using multiple geometric severity descriptors. Among these, aneurysm volume produces the most informative latent representation, with non-interaction graph entropy demonstrating a strong monotonic relationship with severity (Spearman $|ρ| = 0.91$) and generalising to several alternative morphological measures. Finally, we apply the approach to ultrasound-derived flow fields of a left ventricle under varying levels of left ventricular assist device support, where the latent graph captures the progressive loss of coherent vortex interactions under mechanical assistance, demonstrating cross-modal generalisation to imaging data. Across all datasets, latent interaction graphs and graph entropy provide interpretable markers of disease severity and intervention, linking haemodynamic organisation to clinically relevant physiological changes.